Invertibility of linear combinations of two idempotents

Generalized Drazin invertibility of combinations of idempotents

The paper deals with the generalized Drazin invertibility of combinations of idempotents p, q in a Banach algebra. It proves the equivalence of the generalized Drazin invertibility of p−q and p+q, as well as the equivalence of the generalized Drazin invertibility of the commutator pq − qp and anticommutator pq + qp of p, q. It extends several results of J. Math. Anal. Appl. 359 (2009) 731–738, ...

inverse of the linear combinations of two idempotents in the Banach algebra ∗

In this paper, some Drazin inverse representations of the linear combinations of two idempotents in Banach algebra are obtained.

A Survey of Invertibility and Spectrum Preserving Linear Maps

INVERTIBILITY AND FREDHOLMNESS OF LINEAR COMBINATIONS OF QUADRATIC, k-POTENT AND NILPOTENT OPERATORS

Recently, the invertibility of linear combinations of two idempotents has been studied by several authors. Let P and Q be idempotents in a Banach algebra. It was shown that the invertibility of P + Q is equivalent to that of aP + bQ for nonzero a, b with a + b 6= 0. In this note, we obtain a similar result for square zero operators and those operators satisfying x = dx for some scalar d. More g...

Invertibility of switched linear systems

We address the invertibility problem for switched systems, which is the problem of recovering the switching signal and the input uniquely given an output and an initial state. In the context of hybrid systems, this corresponds to recovering the discrete state and the input from partial measurements of the continuous state. In solving the invertibility problem, we introduce the concept of singul...